The problem is with this is that so many priests do it every now and then. If you watch televised Daily Mass, you will probably notice that it's rare to find a priest who doesn't add in his own small addition or subtraction to the Mass. If this is a real problem, it is a rampant problem.

The problem is with this is that so many priests do it every now and then. If you watch televised Daily Mass, you will probably notice that it’s rare to find a priest who doesn’t add in his own small addition or subtraction to the Mass.

Indeed. Almost every Mass I attend has a “small homily,” for the lack of a better term, at the beginning. After a while one doesn’t know whether any of it is actual text of the Mass or whether the bishop allows the addition or what.

When I’m at the Spanish Mass, I’m forever flipping pages to try to follow what the priest says.

I know nothing about the church law on this matter, but I think it is remarkable that so many priests variations of the Mass. Could it be that they are not "wrong," and the law allows these practices, perhaps under the presumption that they are acceptable (that is, acceptable unless proven otherwise)? Can anyone cite church law stating clearly that the order of Mass is not to be altered in the least?

I know nothing about the church law on this matter, but I think it is remarkable that so many priests variations of the Mass. Could it be that they are not “wrong,” and the law allows these practices, perhaps under the presumption that they are acceptable (that is, acceptable unless proven otherwise)? Can anyone cite church law stating clearly that the order of Mass is not to be altered in the least?

Yes.

[59.] The reprobated practice by which Priests, Deacons or the faithful here and there alter or vary at will the texts of the Sacred Liturgy that they are charged to pronounce, must cease. For in doing thus, they render the celebration of the Sacred Liturgy unstable, and not infrequently distort the authentic meaning of the Liturgy.

Some parts of the Mass, the priest is permitted to use his own words. He may, for example, very briefly introduce the Mass of the day after the opening sign of the cross. However unless the Missal specifically allows him to substitute other words, he is obligated to say exactly what is printed in the Missal. When several options exist (like Eucharistic prayer 1, 2, or 3), it’s his choice.

[59.] The reprobated practice by which Priests, Deacons or the faithful here and there alter or vary at will the texts of the Sacred Liturgy that they are charged to pronounce, must cease. For in doing thus, they render the celebration of the Sacred Liturgy unstable, and not infrequently distort the authentic meaning of the Liturgy.

Some parts of the Mass, the priest is permitted to use his own words. He may, for example, very briefly introduce the Mass of the day after the opening sign of the cross. However unless the Missal specifically allows him to substitute other words, he is obligated to say exactly what is printed in the Missal. When several options exist (like Eucharistic prayer 1, 2, or 3), it’s his choice.

The 1975 General Instruction of the Roman Missal (GIRM) had:
“11. It is also up to the priest in the exercise of his office of presiding over the assembly to pronounce the instructions and words of introduction and conclusion that are provided in the rites themselves. By their very nature these introductions do not need to be expressed verbatim in the form in which they are given in the Missal; at least in certain cases it will be advisable to adapt them somewhat to the concrete situation of the community. (Footnote: See SCDW, Circular letter on the Eucharistic prayers, 27 April 1973, no. 14 [DOL 248 no. 1988].)”
(From Documents on the Liturgy 1963-1979, Liturgical Press, Minnesota, 1982, ISBN 0-8146-1281-4).

What exactly were “words of introduction” was probably debatable, but I think they would have reasonably applied to the first three examples Facite gave.

The current 2002 GIRM has replaced this with:

“31. It is also up to the priest in the exercise of his office of presiding over the assembly to pronounce the instructions that are provided in the rites themselves. Where it is indicated in the rubrics, the celebrant is permitted to adapt to some extent these remarks …”

The rubrics do not permit variations with the examples that Facite gave, so varying them is no longer permitted.

Some of the things the GIRM permits:

“23. Moreover, in order that such a celebration may correspond more fully to the prescriptions and spirit of the Sacred Liturgy, and also in order to increase its pastoral effectiveness, certain accommodations and adaptations are specified in this General Instruction and in the Order of Mass.
24. These adaptations consist for the most part in the choice of certain rites or texts, that is, of the chants, readings, prayers, explanations, and gestures that may respond better to the needs, preparation, and culture of the participants and that are entrusted to the priest celebrant. Nevertheless, the priest must remember that he is the servant of the Sacred Liturgy and that he himself is not permitted, on his own initiative, to add, to remove, or to change anything in the celebration of Mass.”

“50. … After the greeting of the people, the priest, the deacon, or a lay minister may very briefly introduce the faithful to the Mass of the day.”

“128. After the Collect, all sit. The priest may, very briefly, introduce the faithful to the Liturgy of the Word.”

Thank you all so very much for your kind and insightful responses. Now what can we, as laity, do to stop this problem? Do we have some kind of moral obligation to tell our pastors to stop this practice?